www.ibr.hi.is
Calendar effect on a small
stock market
Stefán B. Gunnlaugsson
Ritstjórar:
Lára Jóhannsdóttir
Snjólfur Ólafsson
Sveinn Agnarsson
Vorráðstefna Viðskiptafræðistofnunar Háskóla Íslands:
Erindi flutt á ráðstefnu í apríl 2015
Ritrýnd grein
Reykjavík: Viðskiptafræðistofnun Háskóla Íslands
ISSN 1670-8288
ISBN 978-9979-9933-5-3
72
CALENDAR EFFECT ON A SMALL STOCK MARKET
Stefán B. Gunnlaugsson, dósent, Háskólinn á Akureyri
ABSTRACT
In this article, the result of an examination of the efficiency of the Icelandic stock market
is presented. Tests were conducted to find out if the market had shown temporal
anomalies. The findings were that there was a clear relationship between days of the
week and returns. The returns were, on average, negative in the beginning of the week
and positive during the end. On average, returns were lowest on Tuesdays and highest on
Fridays. On the other hand, there was no significant relationship between the months of
the year and stock returns. The so-called “January effect” (i.e., abnormally high returns in
January) was not detected. Returns were, on average, highest in August and lowest in
October.
INTRODUCTION
An efficient stock market is a market where all information is incorporated into the stock price. For
markets to be that efficient, all information must be free in cost and the cost of trading has to be close
to zero. A weaker and more reasonable efficiency is where the marginal benefit of utilising the
information is the same as its marginal cost. Therefore, stock prices follow a random path. The stock
prices change when the markets receive new information, so stock prices are random and unforeseen
(Jensen, 1968).
Stock markets have usually been divided into three categories based on efficiency: weak, semi-strong
and strong efficiency. Weak efficiency means that the stock price contains all previous information
regarding the stock’s price movement and trading volume. Therefore, it is useless to examine the
price development of a stock to predict future price movements. Semi-strong efficiency indicates that
all public information is incorporated into the stock price. Therefore, it is useless to analyse financial
reports and news statements to predict stock price movements. Finally, strong efficiency means that
the stock price includes all information, even information that has not been made public. Therefore,
even insider information is incorporated into the stock price.
A great deal of research has been done on capital market efficiency. Most of the research supports
the efficient market hypothesis or EMH as described above, but some studies have found signs of
capital market inefficiency. The most important signs are:
•
•
•
Temporal anomalies. Studies indicate that average stock returns have been higher in January
than in other months. Across the days of the week, average stock returns have been found to
be lowest on Mondays (Berument and Kiymaz, 2001).
Size. Small stocks, i.e., stocks with small market capitalisation, have outperformed stocks
with large market capitalisation over long periods. The general belief is that small stocks give
superior returns, even when accounting for risk (Fama and French, 1992).
Value vs. glamour. A number of studies have shown that stocks with low price-to-book
ratios, and/or low price-to-earnings ratios, generally called value stocks, outperform stocks
with high ratios, called glamour stocks (Fama and French, 1992).
73
•
Reversals. Several studies have found that stocks that perform poorly in one time period have
a strong tendency to experience sizeable reversals over the subsequent period. Likewise, the
best performing stocks in a given period tend to perform poorly in the following period (De
Bondt and Thaler, 1985).
The Icelandic stock market is small and underdeveloped. One would assume that this small market is
less efficient than other, much larger stock markets, because few parties research the market and it
has fewer stocks and investors. A high number of investors and considerable research are normally
thought to be necessary to make a market efficient.
In this article, the results of a study of calendar effects on the Icelandic stock market are presented.
The study examines the market from the beginning of 1993 until the end of July 2013, thus covering
the bulk of this market’s history. The relationship between days of the week and stock returns is
analysed, as well as the relationship between months and stock returns.
DAYS OF THE WEEK
Previous research
In a study on seven stock markets (Canada, the US, the UK, France, Australia, Japan and Singapore)
from 1969 to 1984, the findings were that stock returns were negative on Mondays in all markets
except for Japan. The findings were statistically significant in the US, UK and Canada. (Condayanni,
et. al. 1987). Research on the US stock market where the SP-500 index was studied from January
1973 until October 1997, found that returns were, on average, negative on Mondays and positive
other days of the week. It was statistically significant that returns were lower on Mondays than other
days (Berument, et. al. 2001). An extensive study on the British stock market from 1988 to 1997
found that returns were negative on Mondays and that there was a statistically significant relationship
between returns and days of the week (Draper, et. al. 2002).
In their research, Agrawal and Tandon (1994) found evidence of market returns shifting based on the
day of the week in the 18 markets they examined. They studied the stock markets in Australia,
Belgium, Brazil, Canada, Denmark, France, Germany, Hong Kong, Italy, Japan, Luxembourg,
Mexico, the Netherlands, New Zealand, Singapore, Sweden, Switzerland and the UK. They found
that the returns were higher than average in most of these countries on Wednesdays and Fridays. The
average returns on Mondays and Tuesdays were, on the other hand, lower than average or negative.
Bayar et. al. (2012) studied the day-of-the-week effect on returns in stock market indices from 19
countries (Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Hong Kong,
Italy, Japan, the Netherlands, New Zealand, Norway, Spain, Sweden, Switzerland, the UK and the
US). The period studied was between 20 July 1993 and 1 July 1998. The findings were that there was
a significant relationship between days of the week and returns in 14 of those markets. A pattern of
higher returns around the middle of the week (Tuesday and Wednesday) and a pattern of lower
returns toward the end of the week (Thursday and Friday) were observed.
Gunnlaugsson (2003) studied the day-of-the-week effect on the Icelandic stock market from 1993 to
2003. He found that returns were, on average, lowest on Tuesdays and highest on Fridays. However,
there was no statistically significant relationship between returns and the days of the week. This
study is a continuation of Gunnlaugsson’s study. It applies the same methodology, but the time series
is longer, and thus should give clear and meaningful results.
But what are the reasons for the day-of-the-week effect findings? One is that negative news often
comes during the weekend. In a study on the US stock market from 1982 to 1986, results showed
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that negative news from firms on the US stock market was more common on the weekend than other
days. Therefore, stock returns on Mondays were lower than other days. Another explanation is that
dividends are more common on Mondays than other days. Many indices do not include returns from
dividends, so they measure lower returns on Mondays than actually occurred (Draper, et. al. 2002).
Data and methodology
The daily returns of the Icelandic stock index were examined. From December 1992 until December
2008, the ICEX15 index was used in the research. That index was made of the 15 most-traded
companies on the exchange. The calculation of this index was terminated at the beginning of 2009
because there was not a sufficient number of stocks listed on the exchange at that time. From 1
January 2009 until 13 August 2013, the OMXI 8 index was used in this study. It is comprised of the
eight most-traded companies on the market. So, this research covers the Icelandic stock market from
the beginning of the year 1993 until 13 August 2013. The data includes 5865 observations.
To analyse if there had been a relationship between days and returns, two tests were applied: the
Kruskal-Wallis test and linear regression. The Kruskal-Wallis test is non-parametric, which means it
does not rely on normal distribution. The test measures the coefficient H, which is defined by this
equation:
( S j − n j (n + 1) / 2)
12
H=
∑
n(n + 1)
nj
2
This test is based on ranking; each observation is ranked from the lowest to the highest. Then the
ranking of each weekday is added up and that sum is S j , j = 1, …,5; n j is the number of all
observations in the group j and n is the total number of observations across all groups. The
distribution of H is a chi square with four degrees of freedom. The null hypothesis is that the
median return of all days is the same. The null hypothesis will be rejected if the H value is higher
than the critical value for the level of significance.
Also, a conventional regression is applied, which is a parametric test and thus relies on normal
distribution. The null hypothesis is that the average return of the index is the same every weekday.
The hypothesis is tested with the following equation, where dummy variables are applied:
Rt = α + β1 D1 + β 2 D2 + β 3 D3 + β 4 D4 + ut
is a dummy variable which has the value 1 on Mondays (i.e., D1=1 if the observation is on
Monday; otherwise it is 0); D2 is a dummy variable for Tuesdays; D3 is a dummy variable for
Thursdays; and D4 is a dummy variable for Fridays. Wednesdays do not have a dummy variable. The
coefficient ut is an error term. The average return of Wednesdays is therefore picked up by the
α coefficient. The average return on other days is the α coefficient plus the β coefficient of that
day. Therefore, the regression measures the difference in the return of that day to the average return
on Wednesdays. Thus, it is possible to test with a t-test if there is a statistically significant difference
in the return of that day and the return on Wednesdays, i.e., the null hypothesis is that the β
coefficient is zero. The null hypotheses are rejected if the t value is lower than -1.96 or higher than
1,96, which is the critical level at the 5% level of significance. The regression also gives the F value
which indicates if the joint explanation of the β coefficients is significant.
Dt
75
Results
Table 1 shows the numerical results. The table shows that the returns were, on average, highest on
Fridays at 0.12% and lowest on Tuesdays at -0.12%. A Shapiro-Wilk test was also conducted to test
the normal distributions of returns. The test was very decisive in the findings that the daily returns
were not normally distributed. That is also evident in the extremely high kurtosis and significant
skewness to the left. Therefore, the extreme negative returns are more common than expected if the
returns were normally distributed. Thus the regression, which results in t and F values which are used
to determine if there is a significant relationship between returns and the days of the week, might not
give meaningful results because of the non-normality of the returns. On the other hand, the validity
of the Kruskal-Wallis test is not affected because it is non-parametric and thus does not rely on
normal distribution.
Table 1: Descriptive statistics of the daily return of the Icelandic
until August 2013.
Monday
Tuesday
Wednesday
Kurtosis
50.9
515.5
13.9
Skewness
-3.27
-20.7
0.98
Standard dev. 1.04%
2.90%
0.97%
Median
0.00%
0.03%
0.05%
Mean
-0.01%
-0.12%
0.06%
stock market from January 1993
Thursday
5.10
-0.23
0.89%
0.03%
0.07%
Friday
4.53
-0.25
0.92%
0.08%
0.12%
The results of the Kruskal-Wallis test gave the H coefficient of 14.28. At the 5% level of significance
and 4 degrees of freedom, the critical value is 9.49. Therefore, the null hypothesis that the median
value of returns is the same each day of the week is rejected, according to this test.
Table 2 shows the main results of the regression. The table does show that there was a significant
relationship between returns and the days of the week during the period studied. The t value for
Tuesday is -2.77, which is highly significant. That means that the average returns on Thursdays were
statistically significantly lower than on Wednesdays. Also, the F value is highly significant, which
indicates that the joint explanations of the beta coefficients were significant. Even though these
results are clear, the fact that the returns were far from being normally distributed does decrease the
validity of this test.
Table 2: The main results of the
January 1993 until August 2013.
Coefficient
α (Wednesday) 0.000391
-0.000471
β 1 (Monday)
β 2 (Tuesday) -0.00159
β 3 (Thursday) 0.000264
0.000806
β 4 (Friday)
F value
4.01
2
R
0.0021
regression of the daily returns of the Icelandic stock market from
t value
1.10
-0.81
-2.77
0.45
1.40
P
0.27
0.42
0.0056
0.65
0.16
0.0029
These results show that returns on the Icelandic stock market are negative on Mondays and
Tuesdays, but significantly better during the second half of the week. There is a clear statistical
relationship between days of the week and returns both in the parametric test (i.e., the regression)
and the non-parametric test (i.e., the Kruskal-Wallis test).
76
The returns were not lowest on Mondays like the findings have been on other foreign stock markets,
but the returns were, on average, slightly negative on those days. Even so, returns on Mondays were
not statistically significantly lower than on Wednesdays. So, it is doubtful that the Icelandic stock
market did show “Monday effects” like many other stock markets have shown. These results are
mostly in line with Gunnlaugsson’s (2003) findings, which were, on average, lower on Tuesdays and
higher on Fridays. The main difference is that this study gives the statistically significant relationship
between days of the weeks and returns.
MONTHS OF THE YEAR
A lot of research on many stock markets has given evidence to higher returns in January than other
months of the year. In an extensive study on the US stock market from 1904 to 1974, an evenly
weighted index was studied, meaning that small stocks had the same weight as large stocks. The
findings were that the average return of this index in January was 3.5%, but other months of the year
it was only 0.5%. It was statistically significant that returns were higher in January than other months
of the year (Rozeff & Kinney, 1976).
In a study on stock markets in 16 countries, the findings were that returns were abnormally high in
January in 15 markets. Higher returns in January occurred in markets where profits on stock sales are
not taxed, i.e., Japan and Canada, but this tax has been named as one of the reasons for higher returns
in January. The returns were also higher in markets where profits on stock sales are taxed, e.g., in the
UK and Australia (Gultekin & Gultekin 1983).
Some research on stock markets has concluded that there has been no significant relationship
between stock returns and months. In an extensive study on the Malaysian stock market from 1992 to
2002, the results were that returns were, on average, highest in February and lowest in March. There
was no “January effect” and there was little relationship between months of the year and returns
(Pandey, 2002). In his study on the Icelandic stock market from 1993 to 2003, Gunnlaugsson (2003)
did not find any relationship between stock returns and month of the year.
The main reason given for abnormally high returns in January has been taxes. In the US and most
other countries, the tax year is the calendar year. It has been suggested that investors sell stocks in
December which have given bad returns to realise losses in order to lower taxes. In January, the
investors buy stocks again, thus resulting in higher returns in January than expected (Jacobs & Levi,
1988).
Data and Methodology
The same methodology and data were applied as when the relationship between days of the week and
returns was examined. Monthly returns of the Icelandic stock index were studied for the period from
January 1993 until July 2013.
To analyse if there was a relationship between months and returns, two tests were applied: the
Kruskal-Wallis test and linear regression. The equation applied in the regression was:
11
Rt = α + ∑ βt Dt + ut
t =1
Rt is the return of the stock index in the month t. D1 is a dummy variable which has the value 1 in
January (i.e., D1=1 if the observation is in January, but otherwise it is 0); D2 is a dummy variable for
77
February; and D3 is a dummy variable for March. Other months of the year get a dummy variable in
the same way. The only exception is July, which does not have a dummy variable because of the risk
of multicollinearity of the independent variables.
Results
Table 3 shows the main descriptive statistics. On average, the returns were highest in August at
3.37% and lowest in October at -4.10%. January had the second highest return of 2.71%, on average,
and April the third highest with 1.78%.
It is obvious looking at the table that monthly returns were not normally distributed. A Shapiro-Wilk
test was conducted to test the normal distributions of returns. The test was very decisive in the
findings that the monthly returns were not normally distributed. The lack of normality is especially
evident in October, with very high kurtosis and very negative skewness. In October 2008, the market
fell 80.8%, which would be almost impossible if the monthly returns had been normally distributed.
Table 3: Descriptive statistics of the monthly return of the Icelandic stock market from January 1993
until August 2013.
Kurtosis
Skew.
St.dev.
Median
Mean
Jan.
Feb.
March
April
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
-0.54
1.40
5.24
7.57
3.06
2.17
-0.98
-0.09
4.99
18.0
1.12
12.22
-0.56
-1.11
-1.95
2.22
1.13
0.47
-0.60
0.17
-1.08
-4.16
-0.82
-3.47
7.70%
5.33%
6.84%
6.09%
7.22%
3.79%
3.97%
6.44%
6.02%
18.47%
5.86%
11.60%
4.64%
2.66%
2.23%
0.59%
-1.0%
0.08%
3.54%
2.05%
-0.62%
0.70%
1.16%
1.86%
2.71%
1.48%
0.67%
1.78%
-0.1%
0.30%
1.51%
3.37%
-0.58%
-4.10%
0.54%
-0.55%
Table 4 shows the results of the regression. The table shows that there was no meaningful
relationship between months of the year and returns during this period. That is indicated by the F
value which is not significant and does indicate that the joint explanation of the beta coefficients is
not statistically significant. The only statistically significant coefficient is in October, but that is
explained by the enormous 80.8% fall in the market in October 2008.
Table 4: The main results of the regression of the monthly return of the Icelandic stock market from
January 1993 until August 2013.
Coefficient t value
P
α (July)
0.0151
0.83
0.41
β 1 (January)
0.0121
0.47
0.64
β 2 (February)
-0.00028
-0.01
0.99
β 3 (March)
-0.00839
-0.33
0.74
β 4 (April)
0.00270
0.11
0.92
(May)
β5
-0.0162
-0.63
0.53
β 6 (June)
-0.0121
-0.47
0.64
β 7 (August)
0.0187
0.72
0.47
β 8 (September)
-0.0208
-0.80
0.42
β 9 (October)
-0.0561
-2.16
0.032
β 10 (November)
-0.00967
-0.37
0.71
(December)
β 11
-0.0206
-0.79
0.43
F value
1.08
0.38
R2
0.048
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Because of the non-normality, the non-parametric test, i.e., the Kruskal-Wallis test, is more valid.
The null hypothesis of the test is that the median return was the same for all months. The H
coefficient of the test was 13.04, but the critical value of the 5% level of significance is 19.68.
Therefore, the null hypothesis was not rejected, based on this non-parametric test. It is safe to
conclude that there was not a significant relationship between month of the year and returns on the
Icelandic stock market during the period observed.
CONCLUSION
In this article, the efficiency of the Icelandic stock market was studied. Tests were conducted to find
out if the market had shown temporal anomalies. The findings were that there was a clear
relationship between days of the weeks and returns. The returns were, on average, negative in the
beginning of the week and positive during the end. On average, returns were lowest on Tuesdays and
highest on Fridays. Therefore, one cannot assume that the Icelandic stock market had the typical
“Monday effect” with significantly lower returns on Mondays than other days of the week, even
though there was a significant relationship between returns and weekdays.
On the other hand, there was no significant relationship between the months of the year and returns.
The so-called “January effect” (i.e., abnormally high returns in January) was not detected. Returns
were, on average, highest in August and lowest in October.
Looking at these results, one could conclude that the tiny Icelandic stock market was efficient and
perhaps more efficient than larger stock markets where abnormally low returns on Mondays and very
high returns in January have been observed. That is thought unlikely. These results could possibly be
explained by the fact that the reasons which have given rise to these abnormalities in other stock
markets might not apply to the Icelandic stock market. However, further research is needed before
such conclusions can be put forward.
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